Abstract

Purely sequential estimation for unknown mean ($\mu$) in a normal population having an unknown variance (${\sigma }^2$) when observations are gathered in groups has been recently discussed in Mukhopadhyay and Wang (2020 Mukhopadhyay, N. , and Z.Wang . 2020. “Purely Sequential FWCI and MRPE Problems for the Mean of a Normal Population by Sampling in Groups with Illustrations Using Breast Cancer Data.” Sequential Analysis 39 (2):176–213. doi:10.1080/07474946.2020.1766893 [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). In this article, we briefly revisit two fundamental problems on sequential estimation: (i) the fixed-width confidence interval (FWCI) estimation problem and (ii) the minimum risk point estimation (MRPE) problem. However, we substitute the estimators defining the stopping boundaries with newly constructed unbiased and consistent estimators under permutations within each group. These new estimators incorporated in the definition of the stopping boundaries have led to tighter estimation of requisite optimal fixed sample sizes. We have analyzed the first-order and second-order asymptotic properties under appropriate requirements on the pilot size. Large-scale computer simulations and substantial data analysis have validated such first-order and second-order results. The methodologies are illustrated with the help of time series data on offshore wind energy.

摘要

纯序列估计未知均值（$\mu$）在方差未知的正常人群中（${\sigma }^2$）最近在Mukhopadhyay和Wang（2020年 N. Mukhopadhyay和Z. Wang。2020年。“通过使用乳腺癌数据在带有插图的人群中进行抽样，得出正常人群的纯连续FWCI和MRPE问题。” 顺序分析39（2）：176 – 213。doi：10.1080 / 07474946.2020.1766893 [Taylor＆Francis Online]，[Web of Science® ]  ，[Google Scholar]）。在本文中，我们简要回顾了有关顺序估计的两个基本问题：（i）固定宽度置信区间（FWCI）估计问题和（ii）最小风险点估计（MRPE）问题。但是，在每个组内的置换下，我们用新构造的无偏且一致的估计器代替定义停止边界的估计器。这些新的估计器并入了停止边界的定义，导致对所需最佳固定样本大小的估计更加严格。我们已经对飞行员规模的适当要求分析了一阶和二阶渐近性质。大规模计算机仿真和大量数据分析已验证了此类一阶和二阶结果。